Vol. 6, 1920 
MATHEMATICS: J. R. KLINE 
529 
The electromagnetic field is thus obtained by superposing on the usual 
electromagnetic field of a moving electric pole a field derived from a 
type of field, which I have considered elsewhere,^ by writing H for E 
and — E for H. The properties of this additional field may be derived at 
once from the properties of the field described previously by simply inter- 
changing the words magnetism and electricity. 
If (J, g, h) are no longer restricted to be the components of the accelera- 
tion and k is no longer restricted to be c'^ —u^ — v'^- w^, the formulae (3), 
(4) still specify an electromagnetic field in which a line of force is the 
locus of points moving with velocity c in directions specified by a set of 
equations of type (1) and these equations can still be reduced to Riccatian 
equations by means of the substitution (2) . 
In a field of this more general type both electricity and magnetism 
travel away from the electric pole with the velocity of light while in the 
case of a field of Page's type there is an emission of magnetism but no 
emission of electricity. There is, however, no magnetic charge associate 
with the moving electric pole. 
In a field of this general type it is possible when f=g = h = p = q = 
f = 0 f or the points which trace out a line of force to move in one constant 
direction which is the same for all and for there to be no radiation of 
energy even through the electric pole has an acceleration.^ It is possible, 
then, for an electric pole of this more general type to describe a circular 
orbit without radiating energy, as in Bohr's theory of the hydrogen atom. 
In the transition from one circular orbit to another the angular velocity 
{p, q, r) may be different from zero and there may be radiation of the 
type described by Page. 
The weak point of the present theory is that it requires the presence of 
electric and magnetic currents in the space surrounding the electric pole. 
This space in fact contains a continuous distribution of electric and mag- 
netic particles which have been emitted from the moving pole and are 
travelling along straight lines with the velocity of light. 
1 Proc. Nat. Acad. Sci., 6, March, 1920 (115). 
2 Amer. J. Math., 37, 1915 (192); see also Murnaghan, F. D., Ibid., 39, 1917; and 
Johns Hopkins Circular, July, 1915. 
3 Proc. London Math. Soc, (Ser. 2) 18, 1919 (95), paragraph 10. 
A NEW PROOF OF A THEOREM DUE TO SCHOEN FLIES 
By J. R. KuNE 
Department of Mathematics, University of Pennsylvania 
Communicated by E. H. Moore, July 7, 1920 
In a paper recently published in the Transactions of the American 
Mathematical Society, Professor Robert L. Moore^ proved the following 
theorem: If ABCDA is a closed curve, then there exist two sets of arcs 
ai and a2 such that (1) each arc of ai lies wholly within ABCDA except 
